MinT - Information on Result #548075

Information on Result #548075

There is no linear OA(5¹⁴, 29, F₅, 11) (dual of [29, 15, 12]-code), because constructionÂ Y1 would yield

linear OA(5¹³, 17, F₅, 11) (dual of [17, 4, 12]-code), but
- a result by Boukliev, Kapralov, Maruta, and Fukui [i]
linear OA(5¹⁵, 29, F₅, 12) (dual of [29, 14, 13]-code), but
- discarding factors / shortening the dual code would yield linear OA(5¹⁵, 25, F₅, 12) (dual of [25, 10, 13]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(5¹⁴, 17, F₅, 12) (dual of [17, 3, 13]-code), but
      - a result by Hill [i]
    2. linear OA(5¹⁰, 25, F₅, 8) (dual of [25, 15, 9]-code), but
      - discarding factors / shortening the dual code would yield linear OA(5¹⁰, 22, F₅, 8) (dual of [22, 12, 9]-code), but
        constructionÂ Y1 [i] would yield
        linear OA(5⁹, 12, F₅, 8) (dual of [12, 3, 9]-code), but
        bound for almost-MDS-codes with dimension nÂ =Â 3 [i]
        linear OA(5¹², 22, F₅, 10) (dual of [22, 10, 11]-code), but
        discarding factors / shortening the dual code would yield linear OA(5¹², 18, F₅, 10) (dual of [18, 6, 11]-code), but
        residual code [i] would yield OA(5², 7, S₅, 2), but
        bound for OAs with strength kÂ =Â 2 [i]
        the Rao or (dual) Hamming bound shows that MÂ â‰¥ 29 > 5² [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OOA(5¹⁴, 29, F₅, 2, 11) (dual of [(29, 2), 44, 12]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(5¹⁴, 29, F₅, 3, 11) (dual of [(29, 3), 73, 12]-NRT-code)	[i]	Depth Reduction
3	No digital (3, 14, 29)-net over F₅	[i]	Extracting Embedded Orthogonal Array